Numerical simulation of unsteady hypersonic chemically reacting flow

Abstract:

The goal of this research is to develop and evaluate a new algorithm for the numerical solution of the axisymmetric Navier-Stokes equations for unsteady hypersonic flow with chemically reacting gas species. The LU-SGS algorithm with a diagonal approximation to the chemical source Jacobian is extended to encompass a logarithmic form of the species conservation equations. It is then further extended to allow time-accurate calculations without inversion of block diagonal matrices. The algorithm is combined with second-order upwind differencing for convective fluxes and central differencing for viscous fluxes to produce an algorithm which is second-order accurate in space and time. This new algorithm is then applied to both steady and unsteady experimental results by employing both an eight-species, nine-reaction model and a nine-species, nineteen-reaction model for the combustion of hydrogen and oxygen. Excellent agreement is achieved in both cases, confirming the accuracy of the algorithm. The efficiency of the algorithm is then compared with results of other researchers. Its computational expense per iteration is shown to be nearly linear with the number of chemical species, where the expense of other algorithms varies with the cube of the number of species. This advantage is reduced by a slower convergence rate per iteration. Its memory requirements are also shown to be linear with the number of species, where those of other algorithms vary with the square of the number of species. As a result of these properties, the new algorithm is shown to be competitive with other algorithms in terms of computational expense, and vastly superior in terms of memory requirements.